Approximately Equivariant Quantum Neural Network for $p4m$ Group Symmetries in Images
This work addresses the challenge of designing efficient and generalizable quantum neural networks for quantum machine learning researchers, though it is incremental as it applies known equivariance concepts to quantum models.
The authors tackled the problem of poor trainability and generalization in Quantum Neural Networks (QNNs) by proposing equivariant Quantum Convolutional Neural Networks (EquivQCNNs) for image classification under planar p4m symmetry, showing that this approach fosters better generalization compared to non-equivariant models in tasks like phase detection of the 2D Ising model and classification of the extended MNIST dataset.
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing the most suitable architecture of Variational Quantum Algorithms (VQAs), and the problem-agnostic models often suffer issues regarding trainability and generalization power. As a solution, the most recent works explore Geometric Quantum Machine Learning (GQML) using QNNs equivariant with respect to the underlying symmetry of the dataset. GQML adds an inductive bias to the model by incorporating the prior knowledge on the given dataset and leads to enhancing the optimization performance while constraining the search space. This work proposes equivariant Quantum Convolutional Neural Networks (EquivQCNNs) for image classification under planar $p4m$ symmetry, including reflectional and $90^\circ$ rotational symmetry. We present the results tested in different use cases, such as phase detection of the 2D Ising model and classification of the extended MNIST dataset, and compare them with those obtained with the non-equivariant model, proving that the equivariance fosters better generalization of the model.